Lesson 3
Equations for Functions
Problem 1
Here is an equation that represents a function: \(72x+12y=60\).
Select all the different equations that describe the same function:
\(120y + 720x = 600\)
\(y = 5 - 6x\)
\(2y + 12x = 10\)
\(y = 5 + 6x\)
\(x=\frac{5}{6} - \frac{y}{6}\)
\(7x + 2y = 6\)
\(x=\frac{5}{6} + \frac{y}{6}\)
Solution
For access, consult one of our IM Certified Partners.
Problem 2
- Graph a system of linear equations with no solutions.
- Write an equation for each line you graph.
Solution
For access, consult one of our IM Certified Partners.
(From Unit 4, Lesson 13.)Problem 3
Brown rice costs $2 per pound, and beans cost $1.60 per pound. Lin has $10 to spend on these items to make a large meal of beans and rice for a potluck dinner. Let \(b\) be the number of pounds of beans Lin buys and \(r\) be the number of pounds of rice she buys when she spends all her money on this meal.
- Write an equation relating the two variables.
- Rearrange the equation so \(b\) is the independent variable.
- Rearrange the equation so \(r\) is the independent variable.
Solution
For access, consult one of our IM Certified Partners.
Problem 4
Solve each equation and check your answer.
\(2x+4(3-2x)=\frac{3(2x+2)}{6}+4\)
\(4z+5=\text-3z-8\)
\(\frac12-\frac18q=\frac{q-1}{4}\)
Solution
For access, consult one of our IM Certified Partners.
(From Unit 4, Lesson 6.)